innovest(x,pdq:vector(p,d,q) [,maxlag:m] [,degree:degree]\ [,polish:T,cycles:nc] [,checkroots:F] [,silent:T] [,arsign:Arsign]\ [,masign:Masign]), integers p>=0, d >= 0, q >= 0, maxlag >= p+q, degree, nc >= 1, Arsign and Masign = +1 or -1. Value is structure(phi:phihat, theta:thetahat, xtxinv, nobs:n, npar, rss:residSS, neg2logL:-2*log(likelihood), aicc:AICC) |

innovest() is a macro to compute the innovations preliminary estimate of coefficients for an ARIMA(p,d,q) time series as described on pp 151-153 of Brockwell and Davis. Keywords 'arsign' and 'masign' allow you to specify the sign convention to be used in defining parameters. See below. innovest(x, pdq:vector(p,d,q) [,maxlag:M]), where x is a REAL vector and p, d and q are nonnegative integers return a structure summarizing the results of the preliminary innovations estimates for an ARIMA(p,d,q) model fit to x. M >= p + q is an integer with default value p + q + max(15, p + q). See below for the form of the results. There is currently no provision for estimating seasonal ARIMA models innovest() creates the following side effect variables COEF = vector(phihat,thetahat), the estimated AR and MA coefficients ALLRESIDUALS = residuals from fitted model including backcast residuals RSS = sum(ALLRESIDUALS^2) NEG2LOGL = -2*log(likelihood) using the estimates found NPAR = p + q + degree + 1 = number of coefficients estimated There are several optional keyword phrases which affect what innovest() does: degree:d1 A polynomial trend of order d1 is removed (after differencing when d > 0). Nothing is removed, not even a mean, when d1 < 0. The default for d1 is -d (mean removed when d = 0, nothing otherwise). polish:T The estimates are adjusted by one or more cylcels of an approximate iteration in the direction of the least squares estimates. cycles:nc nc > 0 an integer, default 1 is the number of "polishing" cycles. checkroots:F suppresses checking for stationarity and invertability silent:T suppress warning messages arsign:Arsign +1 or -1; alters definition of AR paramaters; see below masign:Masign +1 or -1; alters definition of MA paramaters; see below innovest() returns as value structure(phi:phihat, theta:thetahat, nobs:n, xtxinv:xtxinv, npar:p+q+d1+1, rss:residSS, neg2logL:-2*log(likelhihood),aicc:aicc) phihat and thetahat are the estimated AR and MA coefficients (NULL when p or q is 0). xtxinv is NULL without polish:T or when p = q = 0, Otherwise xtxinv is an analogue of the regression solve(X' %*% X) derived from the final polishing step. Its diagonal elements can be used to compute approximate standard errors of the coefficients. residSS = sum of squares of all residuals, including those backcast. The likelihood is the normal likelihood computed using backcasting and includes a factor of (2*PI)^(-n/2) and aicc is a modification of Akaike's information criteria (AIC). Note that innovest() does not return a mean or other estimates of detrending parameters. By default, estimated AR and MA coefficients are checked to see if they define stationary (causal) and invertable operators, respectively. If they do not, a warning message printed and any "polishing" cycles (see below) are suppressed and components rss, neg2logL and aicc of the result are set to MISSING. See topic 'MASIGN' for information on how Arsign (default -1 or the value of ARSIGN if it exists) and Masign (default -1 or the value of MASIGN if it exists) modify the definitions of the AR and MA parameters. To use the convention used by Brockwell and Davis before you start the analysis, you should use Cmd> MASIGN <- 1; ARSIGN <- -1 The convention used by Box and Jenkins (the default) corresponds to Arsign = -1, Masign = -1. See also arima(), hannriss(), innovations().

Gary Oehlert 2003-01-15